MATHEMATICAL ACROPOLIS
Lefteris Kaliambos (Natural Philosopher in New Energy) December 21, 2019 Following the publication on WIKIA of my articles " PARTHENON MATH AND GREAT PYRAMID ", “ΠΑΡΘΕΝΩΝΑΣ ΧΡΥΣΗ ΤΟΜΗ” (Parthenon golden section) , and " MATHEMATICS OF CARYATIDS ", it is now known worldwide that the golden section in Parthenon and in Caryatids, given by Φ = α/β = (α + β)/α , was designed by the great Greek sculptor and mathematician Phidias (ΦΕΙΔΙΑΣ), since the golden number Φ was established in mathematical science taking into account the first letter of the name ΦΕΙΔΙΑΣ. For example, the golden section Φ = α/β in the Parthenon results from the heights (α ) and (β) as shown in the picture of the Mathematical Parthenon. Also (α) as shown in the picture of Mathematical Caryatids expresses the height of each Caryatid, while the height (β) expresses the height of each pedestal. After all, the combinatorial method that led me to the discovery of Acropolis mathematics surprisingly revealed that the small inclination of the columns of the Parthenon was designed by Phidias to form a pyramid over the Attic sky with height (H) extending to the sky above the Goddess of Wisdom. This theoretical height after the application of geometry and the performance of algebraic operations is given by the following mathematical relation, which also contains the mathematics of the golden number Φ0.5 = 1.272… H = a3Φ0.5/(3y) 2 = 1811.3 m. That is, such a celestial pyramid above the temple of the Parthenon with the width of the temple y = 30.88 m should contain not only the values of the sides y and a = 230.34 m, of the great pyramid of Egypt, but also the square root Φ0.5 = 1,272... of the golden number Φ = 1.618… given by the mathematical relation Φ = (1 + 50.5 ) / 2 The golden number Φ which in the Pythagorean years was enriched with the harmonic proportions of the so-called golden section Φ = α/β = (α + β)/α , as shown in the picture of the Mathematical Parthenon and the Mathematical Caryatids, was revealed after a detailed study of minimal geometrical elements, as they were left after so many vandalisms over the centuries, and we do not yet know whether the return of the Parthenon's sculptures contributes to the completion of a mathematical study honoring the entire human race. In fact, all the treasures of Attic architecture of the classical times are concentrated on the sacred rock of the Acropolis of Athens. All buildings erected from 447 BC. to 406 BC such as the Parthenon, the Propylaea, the temple of Athena Nike, and the Erechtheion with the Caryatids, were planned in the years of the Athenian state of Pericles, and as he managed to achieve an unprecedented expression of democracy, so too Parthenon is now the glittering projection of the Athenian state itself. And of course, after the revelation of mathematics in the Parthenon and the Caryatids, today the whole sacred rock could also be called "MATHEMATICAL ACROPOLIS", because above it reveals the gigantic artistic conceptions of ancient Greeks in the mathematics of Pythagoras, since they contain the harmonic proportions of integers 3 and 4, as well as the value of Φ of the golden section. According to the History of the Greek Nation (volume Γ2 page 280) by the artistic staff of Pericles, we know the names of the architects Iktinos, Mensikleus and Kallikrate as well as Phidias. Note that Phidias as a famous sculptor and mathematician had much greater jurisdiction. A detailed analysis of the geometrical data shows that in addition to the mathematics of the golden section, Pheidias also used Pythagorean integers 3 and 4 to discipline the architectural form at a basic mathematical ratio of 32/4 = 9/4, since the length of the pillar to its width are in relation to 9/4, while the same relation regulates the axis of the columns to the diameter. That is, 4.296 m / 1.905 m = 2.25 = 9/4. Also from the width of the temple (y = 30.88 m) and the height (z = 13.724 m) we find the ratio y/z = 9/4, as well as the length of the temple (x = 69.48 m) and its width (y = 30.88 m) we find the same mathematical relation, that is x/y = 9/4. Here we also find that x/z = 92/4 2 = 81/16 = 5.0625 since 69.48 / 13.724 = 5.0625. Really using the ratios y/z = x/y = 9/4 after algebraic operations we will get x = y2/z or x/z = (y2 z) /z = y2/ z2 = 92/4 2 = 81/16 = 5.0625 . In other words, for the determination of the three dimensions x, y and z of the House of the Goddess of Wisdom, the mathematician Phidias should, in addition to architectural harmony, use such proportions of Pythagoras' mathematics to include the mathematics of algebraic equations which led to the fundamental concepts of mathemetics and of physics. ( CORRECT HISTORY OF MATH ). Moreover in order to understand the mathematics of the golden number of Egyptians, we present also in this picture the sacred conical pyramid of Egypt with radius r = a/2, h height and side S (slant height). Historically, both the Babylonians and the Egyptians have been surprised to find that the diagonal δ = 1,618 .. of a regular pentagon with side α = 1 (unit of length) is given by the relation δ + 1 = δ 2 , since 1,618 + 1 = 2,618 = (1,618) 2 So if we write δ = Φ then from the relation Φ 2 = Φ + 1 we can construct a sacred cone by writing S = rΦ, so the height h will be h = rΦ 0.5 = (a/2) Φ0.5 because with the use of the Pythagorean theorem we will get S2 = h2 + r2 or r2Φ 2 = r 2(Φ0.5)2 + r 2 That is, in a very simple sacred cone, the relation Φ 2 = Φ + 1 will apply as long as the radius of the cone is equal to the unit of length (r = 1). In this case the height h will be h = Φ0.5 . So by applying the Pythagorean theorem to the dimensions of the Great Pyramid of Egypt and the mathematics of the golden section I was able to discover that the height h = 146.5 m of the Great Pyramid results from the relation h = rΦ0.5 = (a/2)Φ0.5 = (230.34 /2) (1.272 ..) = 146.5 m. Such a mathematical relation containing the golden number Φ of Egypt as the first letter of the name of Phidias was certainly known to Phidias. Αcording to historical sources Phidias was very familiar with the mathematics of the golden section. After all, in the History of the Greek Nation (volume Δ page 104) we read that Greek cultural life in Egypt existed even before Alexander's arrival, as at least two Egyptian papyri testify. So based on the x, y, and z dimensions of the temple, where the relationships y/z = x/y = 9/4 gave full architectural harmony to the temple, Phidias preferred to give a slight slope to the columns so that the theoretical union of their extension to the Attic sky would form at a very high height (H = 1811.3 m) a celestial pyramid above the Goddess of Wisdom as a divine pyramid analogous to the great pyramid of Egypt. That is, for the theoretical Pyramid of the Parthenon with height (H) and base area E = xy, modern research has shown that the volume VT = (1/3)xyH of the Parthenon theoretical pyramid is half the volume VG = (1/3)a2h of the mathematical Great Pyramid . So because in the Parthenon we observe the simple relation x = 9y/4, while in the Great Pyramid I found the relation h = (a/2)Φ0.5 then by performing algebraic operations I was able to calculate the theoretical height (H) over the Parthenon by writing VT =(1/3) (9y /4)yH = (1/12) (3y)2H VG = (1/3)a 2(a/2)Φ0.5 = (1/6) a3Φ0.5 And because VT = VG/2 we can write (1/12) (3y)2 H = (1/12) a3Φ 0.5 That is, H = a3Φ0.5/(3y)2 or H = (230.3)3(1.272..) / 9(30.88) 2 = 1811.3 In conclusion we would say that Pheidias as an excellent mathematician and as a mature craftsman was inspired by the new spiritual currents of his time and made a decisive move towards fruitful innovations, containing not only a synthesis of Greek Doric and Ionic architecture but also their primitive civilizations of Babylon and Egypt and reached the Pythagorean years, where they were enriched with harmonious proportions in order to mathematically store the Athenian state with the divine or substance of the Goddess of wisdom. Category:Fundamental physics concepts